The level of "superstar" in some of the people mentioned in the replies above is rather questionable. Joan Jett.? lol. she was one hit wonder. Ronnie James Dio was well known but not as popular solo as he was in Black Sabbath. Robert Palmer and Todd Rundgren were well known stars in their own right, but never really became "superstars".
To me a superstar is someone who is a househould name, a person practically everyone has heard of, whether they are music fans or not. The original poster asked for examples of people who became "superstars", not just slightly well known. In that case there are very few, as he said. Ozzy is a household name. The individual members of the Beatles as well. Eric Clapton of course started out in several bands and he qualifies as a superstar in his own right.
That all said, here are some of my picks, the first group went on to become bonafide superstars, and the second group are just people who became as least better known than they were in their original bands.
Superstars
----------
Eric Clapton (after The Yardbirds, Bluesbreakers, Cream and Blind Faith)
Neil Young (after Buffalo Springfield and CSNY)
Rod Stewart (after the Faces and Jeff Beck Group)
Peter Frampton (after leaving Humble Pie)
Steve Winwood (after Spencer Davis Group, Traffic, Blind Faith)
Van Morrison (after "Them")
Others who became better known than they were
------------------------------------------------
Billy Idol (after Generation X)
Chris Cornell (after Soundgarden)
Bob Marley (after the original wailers left)
Morrissey (after the Smiths)
Mike Macdonald (after the Doobie Brothers)
Stevie Nicks (stayed equally famous as Fleetwood Mac in her solo career)
Kenny Loggins (after Loggins & Messina)
Hybrid Mode
